At the Request of AnotherJake:The Game-Oriented List of Game Engines, APIs, Libraries, Frameworks, Middleware, and Vaporware:

Game Engines:

Dim3
Link: http://www.klinksoftware.net
Target: Beginners
Language: Javascript
Pros:
— Easy to use
— VERY helpful community
— Great to start out with
— Well documented
Cons:
— Scripting is somewhat of a mess
— Your game will pretty much be a first-person shooter, anything else feels more of a hack

OGRE
Link: http://www.ogre3d.org/
Target: Advanced
Language: C++
Pros:
— It does 4 variants of shadows, many other effects, handles culling, handles animation from blender, does the dishes, hangs the laundry
Cons:
— Did I mention it does the dishes?
— C++ only

OpenSceneGraph
Link: http://www.openscenegraph.org/
Target: Moderately Advanced and up
Language: C++
Pros:
— Built as a project focused on OpenGL
— It is more focused than OGRE, and faster
Cons:
— C++ only
— Has some issues with multiple monitors and fullscreen
— Its still a beast of an API

OGv1 aka "Broken"
Link: http://log.ep-7.net/?p=3
Target: The DIY guy
Language: C99
Pros:
— Highly flexible
— Clean as possible
— There are effect libraries in works
Either Way:
— I made it
Cons:
— You've got to be willing to do all the effects yourself

I'd like to link my 2D game engine and the game development tool / IDE I'm working on. Both of these are still private and closed-source but it would be nice to increase awareness of them and see if there's any interest in a public release.

Forge (Current internal name)
Link: http://sound-of-silence.com/matt/?page=forge
Target: Beginner
Description: Mac game creation tool / IDE
API: Custom IDE with BASIC-like scripting language
License: TBD
Pros: Simple and easy to get games up and running quickly. Flexible but easy-to-learn scripting language and scene/object based system ideal for adventure games but capable of making platformers, arcade games, etc. Additional support for AppleScript, etc. will make simple general Mac utilities also a possibility.
Cons: Still in the works

Demo video showing a WYSIWYG level editor built with BravoSprites; it features an interactive console, easy terrain creation, sprite creation, and instant play testing: